A Vaccine (CDX-1401) With or Without a Biologic Drug (CDX-301) for the Treatment of Patients With Stage IIB-IV Melanoma

Inclusion Criteria: * Patients with fully resected stage IIb through IV melanoma, with melanoma validated by histology or cytology, who have NOT received prior therapy. * Patients may have had primary cutaneous, mucosal, or ocular melanoma or metastasis from an unknown primary site. * Tissue should be submitted for evaluation of NY-ESO-1 expression and T-cell infiltrates. However, availability of tissue and/or positivity for NY-ESO-1 is not mandatory. * Prior radiation, chemotherapy or biologics NOT allowed * Not currently receiving any anticancer therapy * Age \>= 18 years * Because no dosing or adverse event (AE) data are currently available on the use of CDX-1401 or CDX-301 in patients \< 18 years of age, children are excluded from this study, but will be eligible for future pediatric trials. * Eastern Cooperative Oncology Group (ECOG) performance score of 0-1 * Life expectancy of at least 6 months * Leukocytes \>= 3,000/mcL * Absolute neutrophil count \>= 1,000/mcL * Platelets \>= 75,000/mcL * Hemoglobin \> 9 g/dL * Total bilirubin \< 1.5 x institutional upper limit of normal (bilirubin \< 3 x institutional upper limit of normal for Gilbert's syndrome) * Aspartate aminotransferase (AST)(serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT)(serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x institutional upper limit of normal * Creatinine \< 1.5 x institutional upper limit of normal OR creatinine clearance \>= 60 mL/min/1.73 m\^2 …